Question

a principle of $4000 is invested at 8.25% intrest, compounded annually. How many years will it take accumulate $11,000 or more in the account

Answer 1

for compounded annually

`A=P(r+1)^t`
A=amount total (future)
P=present amount
r=rate in decimal
t=time in years


given
A≥11000
P=4000
r=8.25%=0.0825
t=t
solve
11000≥4000(0.0825+1)^t
divide both sides by 4000
11/4=(1.0825)^t
take the ln of both sides
ln(11/4)=ln(1.0825^t)
ln(11/4)=t(ln(1.0825))
divide both sides by ln(1.0825)
(ln(11/4))/(ln(1.0825))=t
evaluate
12.76=t
it will take 12.76 years, or, to the nearsest whole year, 13 years